Help for Forcing Chains (AKA Kraken rows/columns/cells)
 

Forcing chains refer to two or more AICs starting from a region which all result in a number elsewhere being false. A region refers to a set of candidates such that one must be true. Such sets are:

  • Singles:
    • A single unsolved candidate is either true or false (or a cell contains 2 candidates)
  • Doubles:
    • There are only two instances of a number in a row, column or box.
  • Triples:
    • There are only three instances of a number in a row, column or box.
    • There is a cell with three candidates.
  • Quads:
    • There are only four instances of a number in a row, column or box.
    • There is a cell with four candidates.

    Each candidate in the set is in turn set to 'true', and all the AIC's (simple or complex) that can be generated from this digit are stored in an array. Then the arrays are checked to see if in each case there is a cell that has a digit true, allowing that number to be assigned to that cell. Alternatively, if in each case there is a cell that has a digit false, then that number can be eliminated from that cell.

    An example is Top_95 puzzle 7. After basic moves and a finned X-wing, the following results. The next step is a Kraken row:


    Whichever of the 7's at r2c1234 is true, the 6 at r6c2 is false:

    chain 1: (7)r2c1 - r123c2 = (7-2)r8c2 = (2-6)r6c2
    chain 2: (7-5)r2c2 = r2c3 - r456c3 = (5-6)r6c2
    chain 3: (7)r2c3 - r123c2 = (7-2)r8c2 = (2-6)r6c2
    chain 4: (7)r2c4 - r1c6 = (7-6)r5c6 = r6c6 - r6c2

    After several more similar Kraken rows the puzzle is solved.